Question: Simplify the following expression: $ r = \dfrac{n}{-n - 5} - \dfrac{-7}{5} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5}{5}$ $ \dfrac{n}{-n - 5} \times \dfrac{5}{5} = \dfrac{5n}{-5n - 25} $ Multiply the second expression by $\dfrac{-n - 5}{-n - 5}$ $ \dfrac{-7}{5} \times \dfrac{-n - 5}{-n - 5} = \dfrac{7n + 35}{-5n - 25} $ Therefore $ r = \dfrac{5n}{-5n - 25} - \dfrac{7n + 35}{-5n - 25} $ Now the expressions have the same denominator we can simply subtract the numerators: $r = \dfrac{5n - (7n + 35) }{-5n - 25} $ Distribute the negative sign: $r = \dfrac{5n - 7n - 35}{-5n - 25}$ $r = \dfrac{-2n - 35}{-5n - 25}$ Simplify the expression by dividing the numerator and denominator by -1: $r = \dfrac{2n + 35}{5n + 25}$